She only knows poverty in theory.

Literal

She [topic-は] theory [possessive-の] above [only-でしか] poverty [object-を] does-not-know.

理屈の上でしか~ない means 'only in theory / only on paper.' しか~ない is the restrictive 'only' pattern requiring a negative predicate. 理屈 (りくつ, 'logic, theory, reason') is combined with の上で ('on, in terms of') to mean 'in theoretical terms.'